The only thing Obama could do right now to save himself is to tell the American people that he is going back to the drawing board when it comes to health care. He created a very high attraction value for himself but established no comfort or trust. That takes time. The American people will not tolerate a young and new president radically changing things when he has no track record of success.
In a way this has nothing to do with ideology. It has everything to do with the American people rejecting policies by a new president that may possibly affect them significantly. They love him but they DON'T trust him with their health care. The public is yelling at Obama to get the hell out of their health care and he keeps pushing forward. He is completely out of touch.
A man and a women have been talking for ten minutes at a social event and the women is already attracted to the man. The man sees this and asks her to come back to his place. The women is completely turned off by this because she has no trust in this man and cannot believe that this guy is so out of touch with this simple social rule. The arrogant man pushes forward telling the women what he wants to do to her and even further alienates the women until she leaves. Obama is doing that to the American public.